Bibtex has nothing to do with TEXINPUTS. As you can see here from the file /usr/lib/texmf/web2c/texmf.cnf, bibtex is supposed to listen to its own variables:
% BibTeX bibliographies and style files.
BIBINPUTS = .:$texmfloc/bibtex/bib//:$TEXMF/bibtex/bib
BSTINPUTS = .:$texmfloc/bibtex/bst//:$TEXMF/bibtex/bst
--
Dirk Eddelb"uttel http://qed.econ.queensu.ca/~edd
